𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Coloring linear orders with Rado's partial order

✍ Scribed by Riccardo Camerlo; Alberto Marcone

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
146 KB
Volume
53
Category
Article
ISSN
0044-3050

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

Let βͺ―~R~ be the preorder of embeddability between countable linear orders colored with elements of Rado's partial order (a standard example of a wqo which is not a bqo). We show that βͺ―~R~ has fairly high complexity with respect to Borel reducibility (e.g. if P is a Borel preorder, then P ≀~B~ βͺ―~R~), although its exact classification remains open. (Β© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

πŸ“œ SIMILAR VOLUMES

Rado's selection principle: applications
Rado's selection principle: applications to binary relations, graph and hypergraph colorings and partially ordered sets
✍ Miroslaw Truszczynski; Zsolt Tuza πŸ“‚ Article πŸ“… 1992 πŸ› Elsevier Science 🌐 English βš– 917 KB

Three formulations and various consequences of a compactness principle are given. For example it is shown that an infinite partially ordered set has the jump number at most k if and only if none of its finite subsets has the jump number greater than k. Other applications include Ramsey-type results

Similarity relations, fuzzy linear order
Similarity relations, fuzzy linear orders, and fuzzy partial orders
✍ Sukhamay Kundu πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 230 KB

We show that for a fuzzy partial order R on a ΓΏnite universe , there is a ΓΏnite family of fuzzy linear orders {Li: 16i6k} such that R(x; y) = min{ L i (x; y): 16i6k} for all x and y. This generalizes a well-known result on crisp partial orders, which states that each partial order on a ΓΏnite set is